Welcome to my page
My name is Ishaan Bhadoo, and I am a PhD student in Mathematics at the University of Cambridge. I work in probability theory under the supervision of Professor Wendelin Werner. I am funded by the Gates Cambridge Scholarship.
My interests include percolation, random walks, cover and meeting times, the Gaussian free field, Brownian loop soups, and related questions in random geometry and statistical mechanics.
Email: ishaanbhadoo@gmail.com · ib530@cam.ac.uk
Education
Trinity College, University of Cambridge, PhD in Mathematics, 2025–
Advisor: Professor Wendelin Werner. Funded by the Gates Cambridge Scholarship.
Trinity College, University of Cambridge, Master of Advanced Study (Part III) in Mathematics, 2024–2025.
Thesis: Random Walk on Dynamical Percolation. Advisor: Professor Perla Sousi.
Indian Statistical Institute, Bangalore, Bachelor of Mathematics (Honours), 2021–2024.
First division with distinction.
Research
Rewiring Markov chain on Brownian loop soups
Joint work with Professor Wendelin Werner; in preparation.
We develop a theory of a natural Markov chain on Brownian loop soups, related to the notion of indistinguishability of bosons, and study its connections to the Gaussian free field.
Percolation of arbitrary words: trees and graphs of isoperimetric dimension greater than two
Joint work with Ritvik Radhakrishnan. [PDF]
We study whether every infinite binary sequence can be embedded in a site-percolation configuration. Extending a theorem of Kesten and Benjamini, we prove the result for locally finite trees (under the natural assumption that the site-percolation threshold is below one half) and for transitive graphs of isoperimetric dimension greater than two. An earlier version of the tree argument is available [here].
Comparison principle for cover times of random walks on dynamical percolation
This work grew out of my Part III thesis under the direction of Professor Perla Sousi. It compares cover times for random walk on dynamical percolation with those of simple random walk and resolves Question 1.12 of Hermon and Sousi (2020).
Critical threshold for regular graphs
Undergraduate research with Professor Subhajit Goswami at the Tata Institute of Fundamental Research. [arXiv:2412.00635]
For a $d$-regular quasi-transitive graph $G$, I prove that $p_c(G)=1/(d-1)$ holds only for trees, and give counterexamples when quasi-transitivity is removed.
Teaching
University of Cambridge — Supervisor
Supervisions for the Part II course Probability and Measure (Michaelmas 2025 and Michaelmas 2026).
Indian Statistical Institute, Bangalore — Undergraduate Directed Group Reading Programme
Mentored first- and second-year B.Math students in:
- Field and Galois Theory, November 2022–January 2023.
- Martingale Theory, May–July 2023, jointly with Sarvesh Iyer.